Chapter 1.4, Problem 2E

To determine

To explain how the equation $|4x-7|=-1$ has no solution without performing any calculation.

Explanation of Solution

Given:

  $|4x-7|=-1$

Concept Used:

Modulus of any number is always positive.

For Example: $\left|2\right|=2$ and $|-2|=2$

Here, the given equation is $|4x-7|=-1$ .

For Left hand side, which is $|4x-7|$ , the expression is always positive no matter whatever the value of $x$ is.

Whereas, for Right hand side, which is -1, the expression is a negative value

Now, when $|4x-7|=-1$ , it means that a positive value is equated to negative value which is mathematically incorrect.

Hence, there will be no solution to the given equation.